Spectral densities of superconducting qubits with environmental resonances

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In this paper we derive the environmental spectral density for flux, phase and charge qubits when each of them is coupled to an environment with a resonance. From the spectral density we obtain the characteristic spontaneous emission (relaxation) lifetimes $T_1$ for each of these qubits, and show that there is a substantial enhancement of $T_1$ beyond the resonant frequency of the environment.
2 pages, 3 figures

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